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    <h1 class="hidden">Algorithms, Part I</h1>

    
    
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	<span data-user-title="Student" data-user-id="2392462"><a href="https://www.coursera.org/user/i/d5815a4cd4778ac4f4aa82d8dc0fc3ce">Wayne Pirtle</a></span>

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<div id="post_678_container" class="course-forum-post-text-container"><p>I have attempted this exercise two times and I have read the book several times about this topic.  I have no idea how the ratio is used to derive the constant b where N^b is the growth number.  On this seed b is stated to be 35/12, where does the 35 come from and where does the 12 come from.  Can  someone please tell me how to derive the constant b for this formula.  I understand that the ratio is derived by t(n)/t(n-1) but after that I am lost.</p></div>
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	<span data-user-title="Community TA" data-user-id="69053"><a href="https://www.coursera.org/user/i/2f0edb686bb74cad9ae3859ef0b7fbc6"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/1208120.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Willem Schaap<span style="padding: 1px 3px 2px; font-size: 10px; font-weight: bold; text-transform: uppercase; background-color: rgb(235, 188, 76); margin: 0px 4px 0px 6px; background-position: initial initial; background-repeat: initial initial;">Community TA</span></a></span>

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<div id="post_802_container" class="course-forum-post-text-container"><p>This can be a bit tricky if you don't know calculus. So <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-1-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-1"><span style="display: inline-block; position: relative; width: 78px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(20.4px 18480px 43.2px -8.6px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-2"><span class="mi" id="MathJax-Span-3" style="font-family: MathJax_Math; font-style: italic;">t</span><span class="mo" id="MathJax-Span-4" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mi" id="MathJax-Span-5" style="font-family: MathJax_Math; font-style: italic; padding-left: 5.1px;">a</span><span class="mo" id="MathJax-Span-6" style="font-family: MathJax_Main; padding-left: 4.1px;">⋅</span><span class="msubsup" id="MathJax-Span-7" style="padding-left: 4.1px;"><span style="display: inline-block; position: relative; width: 24.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-8" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -47.6px; left: 17.4px;"><span class="mi" id="MathJax-Span-9" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">b</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-1">t = a \cdot N^b</script>, you can fill this in for two different numbers of points <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-2-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10"><span style="display: inline-block; position: relative; width: 23px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.4px 18480px 45.8px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-11"><span class="msubsup" id="MathJax-Span-12"><span style="display: inline-block; position: relative; width: 22.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-13" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 14.4px;"><span class="mn" id="MathJax-Span-14" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.4px; vertical-align: -3.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-2">N_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-3-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15"><span style="display: inline-block; position: relative; width: 23px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.4px 18480px 45.8px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-16"><span class="msubsup" id="MathJax-Span-17"><span style="display: inline-block; position: relative; width: 22.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-18" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 14.4px;"><span class="mn" id="MathJax-Span-19" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.4px; vertical-align: -3.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-3">N_2</script>: <br>
<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-4-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(20.4px 18480px 47.6px -8.6px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-21"><span class="msubsup" id="MathJax-Span-22"><span style="display: inline-block; position: relative; width: 14.4px; height: 0px;"><span style="position: absolute; clip: rect(25.4px 18480px 43.2px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-23" style="font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 6px;"><span class="mn" id="MathJax-Span-24" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-25" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mi" id="MathJax-Span-26" style="font-family: MathJax_Math; font-style: italic; padding-left: 5.1px;">a</span><span class="mo" id="MathJax-Span-27" style="font-family: MathJax_Main; padding-left: 4.1px;">⋅</span><span class="msubsup" id="MathJax-Span-28" style="padding-left: 4.1px;"><span style="display: inline-block; position: relative; width: 24.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-29" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; clip: rect(27.9px 18480px 43.1px -8.5px); top: -47.6px; left: 17.4px;"><span class="mi" id="MathJax-Span-30" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">b</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; clip: rect(28.3px 18480px 43px -7.9px); top: -35.4px; left: 14.4px;"><span class="mn" id="MathJax-Span-31" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 23.2px; vertical-align: -5.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-4">t_1 = a \cdot N_1^b</script> <br>
<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-5-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-32"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(20.4px 18480px 47.6px -8.6px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-33"><span class="msubsup" id="MathJax-Span-34"><span style="display: inline-block; position: relative; width: 14.4px; height: 0px;"><span style="position: absolute; clip: rect(25.4px 18480px 43.2px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-35" style="font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 6px;"><span class="mn" id="MathJax-Span-36" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-37" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mi" id="MathJax-Span-38" style="font-family: MathJax_Math; font-style: italic; padding-left: 5.1px;">a</span><span class="mo" id="MathJax-Span-39" style="font-family: MathJax_Main; padding-left: 4.1px;">⋅</span><span class="msubsup" id="MathJax-Span-40" style="padding-left: 4.1px;"><span style="display: inline-block; position: relative; width: 24.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-41" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; clip: rect(27.9px 18480px 43.1px -8.5px); top: -47.6px; left: 17.4px;"><span class="mi" id="MathJax-Span-42" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">b</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; clip: rect(28.3px 18480px 43px -8.3px); top: -35.4px; left: 14.4px;"><span class="mn" id="MathJax-Span-43" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 23.2px; vertical-align: -5.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-5">t_2 = a \cdot N_2^b</script> <br>
Taking the <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-6-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-44"><span style="display: inline-block; position: relative; width: 23px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.2px 18480px 46.8px -8.5px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-45"><span class="mi" id="MathJax-Span-46" style="font-family: MathJax_Main;">log</span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-6">\log</script> yields: <br>
<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-7-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-47"><span style="display: inline-block; position: relative; width: 183px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.2px 18480px 46.8px -8.5px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-48"><span class="mi" id="MathJax-Span-49" style="font-family: MathJax_Main;">log</span><span class="mo" id="MathJax-Span-50"></span><span class="msubsup" id="MathJax-Span-51" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 14.4px; height: 0px;"><span style="position: absolute; clip: rect(25.4px 18480px 43.2px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-52" style="font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 6px;"><span class="mn" id="MathJax-Span-53" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-54" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mi" id="MathJax-Span-55" style="font-family: MathJax_Main; padding-left: 5.1px;">log</span><span class="mo" id="MathJax-Span-56"></span><span class="mi" id="MathJax-Span-57" style="font-family: MathJax_Math; font-style: italic; padding-left: 3.1px;">a</span><span class="mo" id="MathJax-Span-58" style="font-family: MathJax_Main; padding-left: 4.1px;">+</span><span class="mi" id="MathJax-Span-59" style="font-family: MathJax_Math; font-style: italic; padding-left: 4.1px;">b</span><span class="mi" id="MathJax-Span-60" style="font-family: MathJax_Main; padding-left: 3.1px;">log</span><span class="mo" id="MathJax-Span-61"></span><span class="msubsup" id="MathJax-Span-62" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 22.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-63" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 14.4px;"><span class="mn" id="MathJax-Span-64" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-7">\log t_1 = \log a + b \log N_1</script> <br>
<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-8-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-65"><span style="display: inline-block; position: relative; width: 183px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.2px 18480px 46.8px -8.5px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-66"><span class="mi" id="MathJax-Span-67" style="font-family: MathJax_Main;">log</span><span class="mo" id="MathJax-Span-68"></span><span class="msubsup" id="MathJax-Span-69" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 14.4px; height: 0px;"><span style="position: absolute; clip: rect(25.4px 18480px 43.2px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-70" style="font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 6px;"><span class="mn" id="MathJax-Span-71" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-72" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mi" id="MathJax-Span-73" style="font-family: MathJax_Main; padding-left: 5.1px;">log</span><span class="mo" id="MathJax-Span-74"></span><span class="mi" id="MathJax-Span-75" style="font-family: MathJax_Math; font-style: italic; padding-left: 3.1px;">a</span><span class="mo" id="MathJax-Span-76" style="font-family: MathJax_Main; padding-left: 4.1px;">+</span><span class="mi" id="MathJax-Span-77" style="font-family: MathJax_Math; font-style: italic; padding-left: 4.1px;">b</span><span class="mi" id="MathJax-Span-78" style="font-family: MathJax_Main; padding-left: 3.1px;">log</span><span class="mo" id="MathJax-Span-79"></span><span class="msubsup" id="MathJax-Span-80" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 22.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-81" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 14.4px;"><span class="mn" id="MathJax-Span-82" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-8">\log t_2 = \log a + b \log N_2</script> <br>
and subtracting: <br>
<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-9-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-83"><span style="display: inline-block; position: relative; width: 263px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(23.1px 18480px 47.6px -8.5px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-84"><span class="mi" id="MathJax-Span-85" style="font-family: MathJax_Main;">log</span><span class="mo" id="MathJax-Span-86"></span><span class="msubsup" id="MathJax-Span-87" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 14.4px; height: 0px;"><span style="position: absolute; clip: rect(25.4px 18480px 43.2px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-88" style="font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 6px;"><span class="mn" id="MathJax-Span-89" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-90" style="font-family: MathJax_Main; padding-left: 4.1px;">−</span><span class="mi" id="MathJax-Span-91" style="font-family: MathJax_Math; font-style: italic; padding-left: 4.1px;">l</span><span class="mi" id="MathJax-Span-92" style="font-family: MathJax_Math; font-style: italic;">o</span><span class="mi" id="MathJax-Span-93" style="font-family: MathJax_Math; font-style: italic;">g<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="msubsup" id="MathJax-Span-94"><span style="display: inline-block; position: relative; width: 14.4px; height: 0px;"><span style="position: absolute; clip: rect(25.4px 18480px 43.2px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-95" style="font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 6px;"><span class="mn" id="MathJax-Span-96" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-97" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mi" id="MathJax-Span-98" style="font-family: MathJax_Math; font-style: italic; padding-left: 5.1px;">b</span><span class="mo" id="MathJax-Span-99" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-100" style="font-family: MathJax_Main;">log</span><span class="mo" id="MathJax-Span-101"></span><span class="msubsup" id="MathJax-Span-102" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 22.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-103" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 14.4px;"><span class="mn" id="MathJax-Span-104" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-105" style="font-family: MathJax_Main; padding-left: 4.1px;">−</span><span class="mi" id="MathJax-Span-106" style="font-family: MathJax_Math; font-style: italic; padding-left: 4.1px;">l</span><span class="mi" id="MathJax-Span-107" style="font-family: MathJax_Math; font-style: italic;">o</span><span class="mi" id="MathJax-Span-108" style="font-family: MathJax_Math; font-style: italic;">g<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="msubsup" id="MathJax-Span-109"><span style="display: inline-block; position: relative; width: 22.8px; height: 0px;"><span style="position: absolute; clip: rect(24.4px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-110" style="font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.6px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 14.4px;"><span class="mn" id="MathJax-Span-111" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-112" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 20.5px; vertical-align: -5.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-9">\log t_2 - log t_1 = b( \log N_2 - log N_1)</script> <br>
Then it's easy to find <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-10-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-113"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.2px 18480px 43.2px -8.3px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-114"><span class="mi" id="MathJax-Span-115" style="font-family: MathJax_Math; font-style: italic;">b</span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-10">b</script>: <br>
<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-11-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-116"><span style="display: inline-block; position: relative; width: 120px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(17.6px 18480px 53.1px -8.3px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-117"><span class="mi" id="MathJax-Span-118" style="font-family: MathJax_Math; font-style: italic;">b</span><span class="mo" id="MathJax-Span-119" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mfrac" id="MathJax-Span-120" style="padding-left: 7.4px; padding-right: 2.2px;"><span style="display: inline-block; position: relative; width: 83.2px; height: 0px;"><span style="position: absolute; clip: rect(27.9px 18480px 45.7px -8.7px); top: -50.3px; left: 50%; margin-left: -34.5px;"><span class="mrow" id="MathJax-Span-121"><span class="mi" id="MathJax-Span-122" style="font-size: 70.7%; font-family: MathJax_Main;">log</span><span class="mo" id="MathJax-Span-123" style="font-size: 70.7%;"></span><span class="msubsup" id="MathJax-Span-124" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 11px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.1px -8.8px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-125" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -38px; left: 5px;"><span class="mn" id="MathJax-Span-126" style="font-size: 50%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-127" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mi" id="MathJax-Span-128" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">l</span><span class="mi" id="MathJax-Span-129" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">o</span><span class="mi" id="MathJax-Span-130" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">g<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="msubsup" id="MathJax-Span-131"><span style="display: inline-block; position: relative; width: 11px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.1px -8.8px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-132" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -38px; left: 5px;"><span class="mn" id="MathJax-Span-133" style="font-size: 50%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; clip: rect(27.9px 18480px 45.7px -8.7px); top: -32.6px; left: 50%; margin-left: -40.5px;"><span class="mrow" id="MathJax-Span-134"><span class="mi" id="MathJax-Span-135" style="font-size: 70.7%; font-family: MathJax_Main;">log</span><span class="mo" id="MathJax-Span-136" style="font-size: 70.7%;"></span><span class="msubsup" id="MathJax-Span-137" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 16.9px; height: 0px;"><span style="position: absolute; clip: rect(28.1px 18480px 43px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-138" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.1px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -38px; left: 10.9px;"><span class="mn" id="MathJax-Span-139" style="font-size: 50%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-140" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mi" id="MathJax-Span-141" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">l</span><span class="mi" id="MathJax-Span-142" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">o</span><span class="mi" id="MathJax-Span-143" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">g<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="msubsup" id="MathJax-Span-144"><span style="display: inline-block; position: relative; width: 16.9px; height: 0px;"><span style="position: absolute; clip: rect(28.1px 18480px 43px -8.6px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-145" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.1px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -38px; left: 10.9px;"><span class="mn" id="MathJax-Span-146" style="font-size: 50%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; clip: rect(15.7px 18480px 23px -9px); top: -24.1px; left: 0px;"><span style="border-left-width: 83.2px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 1.25px; vertical-align: 0px;"></span><span style="display: inline-block; width: 0px; height: 20px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 31.5px; vertical-align: -11.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-11">b = \frac{\log t_2 - log t_1}{\log N_2 - log N_1}</script></p></div>
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	<span data-user-title="Student" data-user-id="489693"><a href="https://www.coursera.org/user/i/1db9268a81e81d9a22b3436b7bdea6db">Lucas de Castro Oliveira</a></span>

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1 week ago</span></div>

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<div id="post_504_container" class="course-forum-post-text-container"><p>I didn't get yet. Could you explain, how does the professor gets the 2.9999 for b and the -33 for c from the lecture slides ? Thanks.</p></div>
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	<span data-user-title="Student" data-user-id="1020706"><a href="https://www.coursera.org/user/i/ab01cb84685cea69a9627143ac4712fe">Jennifer von Geyer</a></span>

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1 week ago</span></div>

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<div id="post_514_container" class="course-forum-post-text-container"><p>Thanks, that was the puzzle piece I was missing</p></div>
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	<span data-user-title="Student" data-user-id="323882"><a href="https://www.coursera.org/user/i/c9ec78017cfcac56c1620ba4103ae277"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/Photo-on-8-29-12-at-10.02-PM.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Rashmi Banthia</a></span>

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1 week ago</span></div>

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<div id="post_530_container" class="course-forum-post-text-container"><p>Thanks @Willem Schaap, the formula was just perfect ! Helped me understand my wrong answer to the quiz.</p></div>
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	<span data-user-title="Community TA" data-user-id="69053"><a href="https://www.coursera.org/user/i/2f0edb686bb74cad9ae3859ef0b7fbc6"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/1208120.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Willem Schaap<span style="padding: 1px 3px 2px; font-size: 10px; font-weight: bold; text-transform: uppercase; background-color: rgb(235, 188, 76); margin: 0px 4px 0px 6px; background-position: initial initial; background-repeat: initial initial;">Community TA</span></a></span>

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1 week ago</span></div>

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<div id="post_573_container" class="course-forum-post-text-container"><p>@Lucas, I guess calculating the time for two different values of N and using the above formula.</p></div>
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	<span data-user-title="Student" data-user-id="25067"><a href="https://www.coursera.org/user/i/eb5996282e9a1e637225e9ea50e92b81"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/DSC03286_cr.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Pavel Kostenko</a></span>

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3 days ago</span></div>

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<div id="post_917_container" class="course-forum-post-text-container"><p>@Willem
I see that your formula works for case when N2 / N1 = 2</p>

<p>Does your formula works for case when N2 / N1 = 3 ?</p></div>
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	<span data-user-title="Community TA" data-user-id="69053"><a href="https://www.coursera.org/user/i/2f0edb686bb74cad9ae3859ef0b7fbc6"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/1208120.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Willem Schaap<span style="padding: 1px 3px 2px; font-size: 10px; font-weight: bold; text-transform: uppercase; background-color: rgb(235, 188, 76); margin: 0px 4px 0px 6px; background-position: initial initial; background-repeat: initial initial;">Community TA</span></a></span>

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3 days ago</span></div>

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<div id="post_918_container" class="course-forum-post-text-container"><p>Yes, for any ratio.</p></div>
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	<span data-user-title="Student" data-user-id="2510835">
	Lei Wu (Student)	</span>

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1 day ago</span></div>

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<div id="post_1043_container" class="course-forum-post-text-container"><p>thx, with your explains,I know it .</p></div>
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	<span data-user-title="Student" data-user-id="343076"><a href="https://www.coursera.org/user/i/e1d2b509e3a62d4ddfcbebadd789ba47"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/hyzhak-nude.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Eugene Krevenets</a></span>

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16 hours ago</span></div>

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<div id="post_1061_container" class="course-forum-post-text-container"><p>Yeah! It's cool but why don't we use "The method of least squares" (http://en.wikipedia.org/wiki/Least_squares) That frequently used for this kind of problems? </p></div>
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	<span data-user-title="Student" data-user-id="90240">
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6 days ago</span></div>

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<div id="post_1465_container" class="course-forum-post-text-container"><p>thanks willem</p></div>
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	<span data-user-title="Student" data-user-id="321230"><a href="https://www.coursera.org/user/i/e0de7b5257f7aa313182283786aecdf4">Michelle Xu</a></span>

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5 days ago</span></div>

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<div id="post_1708_container" class="course-forum-post-text-container"><p>Thanks, Willem. I understand how the formula is calculated, but I cannot understand how the numbers are calculated. For example, when the first two sizes of N (250 and 500), the running time are zero. How can it has a non-zero ratio of running time? Thanks!!</p></div>
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	<span data-user-title="Community TA" data-user-id="69053"><a href="https://www.coursera.org/user/i/2f0edb686bb74cad9ae3859ef0b7fbc6"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/1208120.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Willem Schaap<span style="padding: 1px 3px 2px; font-size: 10px; font-weight: bold; text-transform: uppercase; background-color: rgb(235, 188, 76); margin: 0px 4px 0px 6px; background-position: initial initial; background-repeat: initial initial;">Community TA</span></a></span>

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5 days ago</span></div>

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<div id="post_796_container" class="course-forum-post-text-container"><p>Choose larger values for N so that you have non zero running time. Good luck!</p></div>
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	<span data-user-title="Student" data-user-id="2448854"><a href="https://www.coursera.org/user/i/03efcc5d3a73a0d154a489a45b9c6e97"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/mypic.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Caroline J. Cook</a></span>

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3 days ago</span></div>

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<div id="post_2028_container" class="course-forum-post-text-container"><p>I still don't understand how to get the ratio.  I end up with really small or negative numbers when I take the log of t   </p></div>
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	<span data-user-title="Student" data-user-id="1608582">
	Fabian Uribe Herrera (Student)	</span>

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2 days ago</span></div>

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<div id="post_964_container" class="course-forum-post-text-container"><p>Caroline,</p>

<p>Try using the last 2 values of the list for N and T (the bigger ones), so your log is greater than 0. </p>

<p>Constant "b" equals to the slope of the logarithmic chart of the data, so to obtain b you are going to use the slope formula which is : m = (y1 - y2)/(x1 - x2)</p>

<p>So  b = (log T1 - log T2) / (log N1 - log N2)</p>

<p>( Remember to use Log Base 2 )</p></div>
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	<span>Anonymous</span>

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<div id="post_1097_container" class="course-forum-post-text-container"><p>Isn't it m = (y2-y1)/(x2-x1)</p></div>
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	<span data-user-title="Student" data-user-id="1608582">
	Fabian Uribe Herrera (Student)	</span>

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2 hours ago</span></div>

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<div id="post_1098_container" class="course-forum-post-text-container"><p>Yes, sorry I inverted the X1,X2 &amp; Y1, Y2 numbers on the formula.</p></div>
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	<span data-user-title="Student" data-user-id="1022946"><a href="https://www.coursera.org/user/i/fbd238c06d92626224a7d51a2120b88c">Stefan Langer</a></span>

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<div id="post_2340_container" class="course-forum-post-text-container"><p>Is it important to use a logarithm to the base of the input increase (e.g. lg for doubling log for 10x etc...) or can I use ln, lg or log for calculating the result?
In other words is the base of importance or does it factor itself out when the input size increases.</p></div>
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	<span data-user-title="Student" data-user-id="25067"><a href="https://www.coursera.org/user/i/eb5996282e9a1e637225e9ea50e92b81"><img src="./seed = 990354 calculating the run time   Algorithms, Part I_files/DSC03286_cr.jpg" style="width: 24px; height: 24px; vertical-align: bottom; margin-right: 5px; border: 1px solid rgb(204, 204, 204);">Pavel Kostenko</a></span>

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<div id="post_1062_container" class="course-forum-post-text-container"><p>I think we should use the same base we used for our log log axis</p>

<p>And we used base 2</p></div>
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